What is the wavelength of light (in m) emitted by a hydrogen atom when an electron relaxes from the 5 energy level to the 1 energy level?
To find the wavelength of light emitted by a hydrogen atom when an electron relaxes from one energy level to another, we can use the Rydberg formula. The Rydberg formula is given as:
1/λ = R_H * (Z^2 / n1^2 - Z^2 / n2^2)
Where:
λ is the wavelength of the emitted light.
R_H is the Rydberg constant for hydrogen, approximately 1.097 × 10^7 m^-1.
Z is the atomic number, which is 1 for hydrogen.
n1 is the initial energy level.
n2 is the final energy level.
In this case, the initial energy level (n1) is 5 and the final energy level (n2) is 1. Plugging these values into the formula, we have:
1/λ = (1.097 × 10^7 m^-1) * (1^2 / 5^2 - 1^2 / 1^2)
Simplifying further:
1/λ = (1.097 × 10^7 m^-1) * (1/25 - 1/1)
1/λ = (1.097 × 10^7 m^-1) * (24/25)
1/λ = 1.0456 × 10^7 m^-1
Now, we can find the wavelength (λ) by taking the reciprocal of both sides:
λ = 1 / (1.0456 × 10^7 m^-1)
λ ≈ 9.563 × 10^-8 m
Therefore, the wavelength of light emitted when an electron relaxes from the 5th energy level to the 1st energy level in a hydrogen atom is approximately 9.563 × 10^-8 meters.